Rota–Baxter paired comodules and Rota–Baxter paired Hopf modules
Volume 168 / 2022
Abstract
We introduce the concept of Rota–Baxter paired comodules, which is dual to Rota–Baxter paired modules defined by Zheng et al. (2020). We discuss some properties of Rota–Baxter paired comodules, in particular we give a characterization of generic Rota–Baxter paired comodules, which has an important application for the construction of Rota–Baxter comodules. Moreover, we construct Rota–Baxter paired comodules on Hopf algebras, weak Hopf algebras, weak Hopf modules, dimodules, relative Hopf modules and Rota–Baxter paired comodules. We also introduce the concept of Rota–Baxter paired Hopf modules by combining the notion of Rota–Baxter paired module with Rota–Baxter paired comodule, and prove a structure theorem for generic Rota–Baxter paired Hopf modules.
